
with \(\beta =(k_{\text{B}}T)^{-1}\)  being the inverse thermal energy. While Braun and Dhont adapted their notion by replacing the free energy of solvation by a more general “reversible work”, there is still a conceptual difference to the Soret coefficient derived by Würger, as that reversible work is still defined as the work needed to remove a solute particle from an isothermal system of temperature \(T\)  and insert it into an isothermal system of temperature \(T+\text{d}T\) , thus making it effectively a free energy of solvation. Following [1]}, a similar argument has been proposed by Eastman. The Soret coefficient can be identified to be proportional to a quantity called “heat of transfer” \(Q^*\)  [2]} which in turn can be expressed in terms of an entropy of transfer \(Q^*=S^*T\) . Eastman identifies this entropy of transfer as the local entropy of solvation and thus reaches Eq. (REF ), dismissing the additional term \(1/T\) . A third route to find the entropy of solvation as the driving force of thermophoresis is to identify the thermodynamical force as \((\nabla \mu )/T\)  and postulate that the Soret equilibrium corresponds to a mechanical equilibrium \(\nabla \mu =0\)  [1]}. Connecting this condition with Eq. (REF ) and dismissing a term \(\ln \rho \,\nabla T\) , one finds again the entropy proportional to the Soret coefficient.
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